## Example

The market for cookies is huge, with many consumers and many sellers.

The supply follows the equation `Q_S = 3 P`.

The demand follows the equation `Q_D = 10 - 2 P`.

In equilibrium, supply equals demand

$$ \begin{align*} Q_S &= Q_D \\ 3 P &= 10 - 2 P \\ 5 P &= 10 \\ P &= 2 \end{align*} $$In equilibrium, a banana is sold $2 and there are 6 bananas on the market.

### Question

The supply equation for bananas is `Q_S = -43 + 24 P`.

The demand is `Q_D = 421 - 34 P`.

What is the equilibrium price? What is the equilibrium quantity?

### Step 1: Equate supply and demand

###
##

$$
\begin{align*}
Q_S &= Q_D \\
-43 + 24 P &= 421 - 34 P \\
34 P + 24 P &= 421 + 43 \\
(34 + 24) P &= 421 + 43 \\
P &= \frac{421 + 43}{34 + 24} \\
P &= 8.0
\end{align*}
$$

$$
\begin{align*}
Q_S &= Q_D \\
-43 + 24 P &= 421 - 34 P \\
34 P + 24 P &= 421 + 43 \\
(34 + 24) P &= 421 + 43 \\
P &= \frac{421 + 43}{34 + 24} \\
P &= 8.0
\end{align*}
$$

### Step 2: Plug into the supply curve (or the demand curve)

###
##

$$
\begin{align*}
Q_S &= -43 + 24 \times 8.0 \\
Q_S &= 149.0
\end{align*}
$$

$$
\begin{align*}
Q_S &= -43 + 24 \times 8.0 \\
Q_S &= 149.0
\end{align*}
$$